Theorems · Definition · combinatorics
SimpleGraph.maxDegree
{V : Type u_1} → (G : SimpleGraph V) → [Fintype V] → [DecidableRel G.Adj] → ℕThe maximum degree of all vertices (and 0 if there are no vertices).
The key properties of this are given in exists_maximal_degree_vertex, degree_le_maxDegree
and maxDegree_le_of_forall_degree_le.
- Defined in
- Mathlib.Combinatorics.SimpleGraph.Finite
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FintypeDecidableRel
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fintypestatement and proof · cited by 7,736
- Finset.univproof · cited by 3,473
- SimpleGraphstatement and proof · cited by 3,072
- SimpleGraph.Adjstatement and proof · cited by 1,346
- Finset.imageproof · cited by 910
- SimpleGraph.degreeproof · cited by 112
- Finset.maxproof · cited by 50
- WithBot.unbotDproof · cited by 49
Cited by19
Results whose statement or proof uses this declaration.
- SimpleGraph.maxDegree_of_subsingletonstatement · cited by 5
- SimpleGraph.Copy.maxDegree_monostatement and proof · cited by 3
- SimpleGraph.exists_maximal_degree_vertexstatement · cited by 3
- SimpleGraph.IsContained.maxDegree_monostatement and proof · cited by 2
- SimpleGraph.degree_le_maxDegreestatement · cited by 2
- SimpleGraph.maxDegree_bot_eq_zerostatement · cited by 2
- SimpleGraph.maxDegree_le_of_forall_degree_lestatement and proof · cited by 2
- SimpleGraph.minDegree_le_maxDegreestatement · cited by 1
- SimpleGraph.IsRegularOfDegree.maxDegree_eqstatement · cited by 1
- SimpleGraph.IsContained.max_degree_lestatement · cited by 0
- SimpleGraph.Copy.max_degree_lestatement · cited by 0
- SimpleGraph.Iso.maxDegree_eqstatement and proof · cited by 0